1. Literary dependence.
For one example, prophecy buffs often claim the crucifixion narratives in the four gospels are some kind of supernatural 'fulfillment' of Psalm xxii, since all of them quote or allude to it and make the connection with Jesus' passion. This is of course ridiculous since all four gospel authors wrote their crucifixion accounts with the text of Psalm xxii before them. That is why certain elements in the psalm are present in them because they had literary access to it and obviously incorporated certain theological motifs in the psalm into their narratives. It isn't genuine prophecy. The psalm itself is not even prophetic.
2. Original context
Take Matthew ii.17, which quotes Jeremiah xxxi.15 in connection with Herod's assault on the infants of Bethlehem, an event most scholars consider non-historical anyway. But even granting this event's historicity, when we look at the quote in its original context in Jeremiah, we find that it has nothing to do with a future event concerning anyone named Jesus or Herod or with infants, but with the depopulation and promised restoration of the tribes of northern Israel (or Ephraim; see verses 16-22). Again, this is not genuine prophecy, and the verse as it stands in Jeremiah is not a prediction of the future but a poetic way to describe the sufferings and captivity of northern Israel during that historical period, not a future period.
Each of the prophecies in the NT 'fulfilled' by Jesus are liable to the same criticisms, and so it's difficult to take the claims for the fulfillment of genuine prophecy in the NT seriously.